1 Introduction

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1 Introduction

1.1 What is metaphysics?

Since this book is called An Introduction to Metaphysics, it makes sense to begin with a short, simple, and clear definition of the word ‘metaphysics’. If only it were that easy. Part of the problem is that it’s practically impossible to get any two philosophers to agree on a single definition of ‘metaphysics’. (And the book is, after all, written by two philosophers.) But there are also issues relating to the strange etymology of the term ‘metaphysics’, and further complications arising from the fact that ‘metaphysics’ has one meaning in ordinary English and another meaning within (academic) philosophy. Nevertheless, we’ll do our best in this section to offer the reader what we take to be a reasonable characterization of the field of metaphysics. In fact, we’ll offer three different but mutually compatible characterizations. Let’s start with what metaphysics is not. Metaphysics – as we are using the term – is not the study of the occult. Nor is it the study of mysticism, or auras, or the power of pyramids. Although the word ‘metaphysics’ may indeed have all of those connotations in ordinary English, the word is used within academic philosophy in an entirely different way. And this book, as it happens, is meant to be an introduction to the branch of academic philosophy that is known as metaphysics. What about the etymology of the word ‘metaphysics’? Can that shed some light on our subject? Well, the current usage of the word has its ori- gins in the ancient world. It seems that during the first century CE, some of Aristotle’s works were being collected and published in Alexandria. (Aristotle had died 300 or 400 years earlier, around 322 BCE.) Among these was a collection of Aristotelian writings that was given a name in ancient

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2 An Introduction to Metaphysics

Greek that is normally translated into modern English as Physics.1 (But the name is misleading: Aristotle’s Physics is not mainly about physics. In fact, ironically, it is mainly about metaphysics.) Shortly after the publication of Aristotle’s Physics, another batch of Aristotle’s writings was ready for publication. The editor in charge of the project gave this other work a title in ancient Greek that means, literally, After the Physics. (This was the equivalent of calling it The Book We Published after We Published Aristotle’s Physics.) Moreover, it just so happened that this other book of Aristotle’s contained discussions of such important but disparate philosophical topics as existence, identity, actuality, potentiality, time, change, causation, substance, matter, form, and universals (among others). Despite the fact that they were all discussed by Aristotle in other works of his (including his Physics), these topics (and others more or less closely related to them) eventually came to be associated with that particular book of Aristotle’s in which they featured so prominently – a book whose Greek name is Metaphusika and whose English name is (you guessed it) Metaphysics. If we take an etymological approach to characterizing metaphysics, then, we will say that metaphysics is the branch of philosophy concerned with a disparate collection of topics that happen to be associated with one particular collection of writings by Aristotle, namely, the collection that was published after Aristotle’s Physics. Unfortunately, this etymological approach doesn’t give us a very sat- isfying account of what many take to be the most central branch of philosophy. It would be nice to be able to give a more conceptual, big-picture account of metaphysics. And indeed, as most metaphysicians will tell you, it’s hard not to have the sense that the various topics within metaphysics do have something essential in common with one another, in much the same way that the various topics within ethics, or the topics within epistemology, have something essential in common. Attempts to capture in a definition this something essential that most metaphysicians feel unifies the various topics of their field often result in somewhat elusive pronouncements like the following: metaphysics is the branch of philosophy concerned with fundamental questions about the nature of reality.

1 All of the works of Aristotle discussed in this chapter can be found in The Basic Works of Aristotle.

Introduction 3

This big-picture approach, unfortunately, is not without its own problems. One main difficulty is that most branches of inquiry, including biology, economics, and history, are also concerned with reality. Perhaps, however, there is an easy way to deal with this problem: let us assume that we all have at least a rough idea of what philosophy is, and that we can safely assert that other reality-based fields, such as biology and so on, are not branches of philosophy. That still leaves the problem of distinguishing metaphysics from other branches of philosophy, such as ethics and epistemology, which are after all also concerned with reality. But now we might be able to take a contrast- ive approach. Here’s the idea. Suppose (as we have already) that we possess a rough idea of what philosophy is. Then we can add some helpful context to our big-picture approach to characterizing metaphysics by saying that there are three main branches of philosophy: ethics (the branch of philosophy concerned with fundamental questions about right and wrong and good and bad); epistemology (the branch of philosophy concerned with fundamental questions about knowledge and justification); and metaphysics (the other main branch of philosophy). In other words, we can characterize metaphysics as what is left over when you subtract ethics and epistemology from the core area of philosophy. But what exactly is left over when you subtract ethics and epistemology from the core area of philosophy? We think a good way to answer this question is with specific examples. Here, then, are some of the topics that metaphysicians deal with: ontology (roughly, the study of being, including the attempt to come up with a list of all the main categories of things that exist); the nature of time; the Mind–Body Problem (roughly, the problem of understanding the relationship between mental phenomena and the physical basis of those phenomena); the problem of personal identity (roughly, the problem of identifying the conditions under which an earlier person and a later person are one and the same person); the problem of freedom and Determinism (roughly, the problem of specifying what is required in order for a person to be acting freely); the nature of the laws of nature; the nature of causation; and the nature of material objects (including questions about the relation between an object and the matter it is made of, and the conditions under which two or more objects compose a further object). If the topics on this list aren’t yet perfectly clear to you, do not despair. We will explore one example of an ontological issue (the existence of properties)

4 An Introduction to Metaphysics

in some depth in Chapter 9 of this book. Each of the other topics on the list is the subject of its own chapter. So by the end of the book you should have a much clearer conception of what each of these topics amounts to. And then you will be in a position to appreciate our third approach to characterizing metaphysics, according to which metaphysics is the branch of philosophy concerned with topics like those listed in the previous paragraph. Let us summarize our discussion so far. We have identified three different approaches to characterizing metaphysics. One is the etymological approach, according to which metaphysics is the branch of philosophy concerned with a disparate collection of topics that just happen to be associated with one particular collection of writings by Aristotle, namely, the collection that was published after Aristotle’s Physics. Next there is the big-picture approach, according to which metaphysics is the branch of philosophy concerned with fundamental questions about the nature of reality. And finally, there is the definition-by-example approach, according to which metaphysics is the branch of philosophy concerned with such topics as ontology, time, the Mind–Body Problem, the problem of personal identity, the problem of freedom and Determinism, laws of nature, causation, and material objects (all of which will be discussed extensively in this book). For the remainder of this chapter, our plan is to do three things. First, in 1.2, we will begin our metaphysical investigations with some basics about modality, especially the concept that philosophers call metaphysical necessity. This will permit us to discuss a topic that plays some role in almost every chapter of the book, and that also serves as a nice illustration of a conceptual problem in metaphysics. Then, in 1.3, we will introduce some basics about ontology. These two sections of this first chapter will let us demonstrate in a very introductory way some of the methods of the metaphysician. And finally, in 1.4, we will end the chapter by trying to set aside a common skeptical intrusion that you, the reader, would do well to resist.

1.2 Modality

Let’s begin with a short list of some propositions that are widely accepted as being metaphysically necessary.2

2 We ‘list’ propositions by displaying sentences that express the relevant propositions.

Introduction 5

Kant is wise or it is not the case that Kant is wise. 2 + 2 = 4. Red is a color. All bachelors are unmarried.

It would be helpful if we could give you a deﬁnition of ‘necessity’ that would make it crystal clear why these are fairly uncontroversial. That’s not so easy to do. About the best we can do is to say that these propositions are metaphysically necessary because they can’t be false, because they have to be true. No matter how our world might be, these four propositions would be true. Propositions that are not metaphysically necessary are ones that are either metaphysically impossible or metaphysically contingent. The metaphysically impossible propositions include:

Kant is wise and Kant is not wise. 2 + 2 = 5. Red is not a color. Not all bachelors are unmarried.

These propositions can’t be true; they have to be false. They would be false no matter what. The metaphysically contingent propositions include:

Kant is wise. There are four oranges in the refrigerator. Red is the color of some ﬁre engines. Asia is the smallest continent.

Metaphysically contingent propositions can be true and also can be false. Whether they are true or false does depend on what the world is like. As you may have already inferred, the metaphysically possible propositions are the ones that are either metaphysically necessary or metaphysically contingent; they are the ones that are not metaphysically impossible. Metaphysical necessity is one concept of necessity. There are others. For example, there is an important class of metaphysically contingent propositions that are physically (i.e., lawfully) necessary. For example, it is not uncommon to hear someone say, “It is impossible that there be a perpetual motion machine.” But when this is said it is not meant that such a machine is metaphysically impossible, that it is somehow contradictory in the way that, say, Kant’s being wise and not wise is. What is meant is that

6 An Introduction to Metaphysics

the existence of a perpetual motion machine would contradict some law of nature (e.g., The Second Law of Thermodynamics). For a quite different sort of example, there is epistemological necessity. Certain propositions are said to be possibly false that in fact are metaphysically necessary. For a long time, it was common to hear mathematicians and others say things like, “It is possible that Fermat’s Last Theorem is false – there has been no proof.”3 Prima facie, what they said was perfectly true. Nevertheless, in the mid-1990s, thanks to the mathematical work of Andrew Wiles, Fermat’s Last Theorem was proven. So, like other mathematical truths, it is metaphysically necessary – and always has been. Evidently, those who said it might be false were not saying that it wasn’t metaphysically necessary. All they were saying was that, for all they knew, or for all anyone knew, Fermat’s Last Theorem was false. They were reporting the epistemological possibility that it was false. There is another epistemological notion worth mentioning here. Considering how it is characterized, you wouldn’t think that there was much chance of confusing it with metaphysical necessity. But in fact it is easy to do, because the two notions in question share many important instances. Many metaphysically necessary propositions are a priori true. That means, very roughly, that they are such that, once the proposition is grasped, it can be known to be true based solely on reason.4 Some perception might be required to grasp the proposition, to acquire the concepts involved, but with a priori true propositions, there is no further need to rely on perception in order to know that the world matches up. The a priori true propositions contrast with propositions that are a priori false (the propositions that can be known to be false by reason alone) and with the propositions that are a posteriori (the ones that are neither a priori true nor a priori false).5 The four examples of metaphysically necessary propositions listed above are all widely accepted as a priori true. The idea is that, if you understand logical terms like ‘and’ and ‘not’, you are already in a position to ﬁgure out

3 Fermat’s Last Theorem is the proposition that xn + yn = zn has no integer solutions for n > 2 and x, y, z > 0. 4 ‘A priori’ is Latin for prior to. The idea is that a priori truths can be known independ- ently of (prior to) experience. 5 ‘A posteriori’ is Latin for behind; a posteriori propositions can be known only with the beneﬁt of experience.

Introduction 7

in your head that Kant is either wise or not wise. You don’t have to have read the Critique of Pure Reason to find that out! Similarly, if in addition to being familiar with some logical concepts, you know what it is to be a bachelor and what it is to be unmarried, then you are already in a position to figure out by reason alone that all bachelors are unmarried. Parallel points could be made about the propositions that 2 + 2 = 4 and that red is a color.6 So the a priori and metaphysical necessity seem a lot alike. Given only the examples we have introduced up to this point, these two philosophical concepts apply to exactly the same propositions. But in other ways these concepts are very different. In particular, though we have given no formal definition of either, the differences in the rough characterizations we have given are pretty severe. Metaphysical necessity was characterized only in terms of having to be true, yet a distinctly epistemological concept – knowledge – was brought in to characterize the a priori. On the face of it, that seems to leave open that these two concepts, the a priori and metaphysical necessity, might not match up about every case. Maybe there are some propositions that are metaphysically necessary but not a priori true. Maybe there are some a priori truths that are not metaphysically necessary. For a long time, the presumption was that these concepts don’t come apart. The thought was that, though they are different concepts with different definitions, they have all the same instances. The reasoning behind this traditional presumption goes something like this: the truth of metaphysically necessary propositions doesn’t depend on how the world is – they have to be true, they are true no matter what – and so their truth must be a purely conceptual matter. If their truth is a purely conceptual matter, then it can be known by reason alone. Meanwhile, if a proposition’s truth is knowable by reason alone, if you don’t need to interact with the world to know that it is true, then its truth must be a purely conceptual matter, and thus it must be necessarily true. Many philosophers have been rethinking the traditional presumption.

Saul Kripke offers that water is H2O is an example of a proposition that is necessarily true but not a priori true.7 It does seem to be necessarily

6 To extend the parallels, our examples of metaphysically impossible propositions are all generally taken to be a priori false, and the examples of metaphysically contingent propositions to be a posteriori. 7 Kripke, Naming and Necessity, pp. 116 ff.

8 An Introduction to Metaphysics

true. How it could be false? Anything that wasn’t composed of two parts hydrogen and one part oxygen just wouldn’t be water. But it also seems

clear that it is a posteriori true. The discovery that water is H2O was not reasoned from reﬂection on the conceptual natures of water, hydrogen, and oxygen. This was an important scientiﬁc discovery made at the end of the late eighteenth century based on experiments that composed water from hydrogen and oxygen. It is hard to see how anyone could have come to know the molecular structure of water based only on reason. The lesson we are trying to impart here is not that Kripke is right. Maybe he is and maybe he isn’t. There is lots of interesting discussion of this example and other examples that Kripke and others have proposed.8 Our

point in discussing the water-is-H2O example is to show that you should not simply assume that the metaphysically necessary propositions and the a priori true propositions match up exactly. We hope we have helped you understand metaphysical necessity better just by citing examples of necessary truths and distinguishing metaphysical necessity from some ordinary notions (physical necessity and epistemological necessity) and an important philosophical one (the a priori).9 But there is more that might be done. When seeking understanding, philosophers often try to provide a philosophical account or theory of the concept in question. A philosophical account can include something like a deﬁni- tion, a full characterization of the concept that is usually reported by a biconditional (an ‘if and only if’) sentence; such an account states a necessary and sufﬁcient condition for the concept to apply. Often, however, philosophical accounts aren’t that ambitious; some theories include only some plausible principle that describes some important feature of the concept. You will run into several philosophical accounts in this book. Here is one simple example about moral freedom from Chapter 3:

Stacean Compatibilism An action is free if and only if it is unconstrained.

And here is another:

Alternative Possibilities S does A freely only if S could have done something other than A.

8 See, for example, Sidelle, Necessity, Essence, and Individuation. 9 Our approach has been similar to the approach taken by Alvin Plantinga in the ﬁrst chapter of The Nature of Necessity.

Introduction 9

All the theories we will consider will be subjected to scrutiny, and we will often ﬁnd disagreement among philosophers about whether the account succeeds. What about necessity? Is there some philosophical account of metaphysical necessity, something that might go beyond what we have done so far by way of introducing you to this crucial concept? There is actually a lot of agreement on one simple treatment. All metaphysicians will accept that something is metaphysically necessary if and only if its negation is not metaphysically impossible. Indeed, this account is already implicit in our discussion above.

Necessity in Terms of Possibility P is metaphysically necessary if and only if not-P is not metaphysically possible.

All metaphysicians will also agree that, though this account is true, it is no great philosophical achievement in an attempt to provide understanding of metaphysical necessity. Notice that one can equally well explain possibility in terms of necessity:

Possibility in Terms of Necessity P is metaphysically possible if and only if not-P is not metaphysically necessary.

Were a metaphysician to accept both the two preceding accounts with no further account of metaphysical necessity or metaphysical possibility, there would be a disappointing circle in his or her philosophy of modality. Also, it would be pretty unusual for someone to perfectly well understand metaphysical necessity and not understand metaphysical possibility. That’s because metaphysical possibility and metaphysical necessity live very close to each other in conceptual space; they are both modal concepts. It is not exactly clear who would be helped by either theory. Is there an account of either metaphysical necessity or metaphysical possibility that would be more illuminating, one helpful to someone who didn’t have any prior understanding of either of these modal concepts? David Lewis took on the challenging task of providing such an account.10 He thought that our world, the universe around us, is one of many. In our world, pigs don’t ﬂy, Rome is the capital of Italy, and no signals travel faster

10 Lewis, Counterfactuals, especially pp. 84–91, and On the Plurality of Worlds.

10 An Introduction to Metaphysics

than light. But, as he saw it, there are other worlds, ones where pigs do ﬂy, Beijing is the capital of Italy, and superluminal travel is commonplace. Take all these other worlds together with our world (the actual world) to comprise the possible worlds. This permits accounts of both metaphysical necessity and metaphysical possibility:

Lewis on Necessity P is metaphysically necessary if and only if P is true in all the possible worlds. Lewis on Possibility P is metaphysically possible if and only if P is true in at least one of the possible worlds.

Thinking of possibility as truth in a possible world is a picturesque and useful way of thinking of possibility, one that we will occasionally adopt when proposing and considering hypothetical examples. Indeed, to introduce a possibility for consideration, philosophers often start by saying, “Consider a possible world where …” Thinking of necessity as truth in all possible worlds is just as picturesque and useful. Lewis, however, did not intend to just be describing an effective man- ner of doing and delivering metaphysics. He took himself to be providing conceptual understanding of metaphysical necessity and metaphysical possibility. Despite how it might look, the biconditionals displayed above are not put forward to account for metaphysical necessity or metaphysical possibility in terms of metaphysical possibility (or any other kind of possibility). For Lewis, there is no circularity in his overall philosophy of modality. ‘The possible worlds’ is just a name for a certain collection of things – big universe-size things, admittedly – that Lewis assumes are just as much part of reality as you are and we are. Indeed, we could have just called them the worlds, and left the word ‘possible’ out of the explanatory parts of the accounts altogether. For a proposition to be metaphysically necessary is for it to be true in all those things, all those worlds. For a proposition to be metaphysically possible is for it to be true in at least one of them. As is true of all the theories that are presented in this book, there are lots of questions that can be asked regarding Lewis’s accounts of metaphysical necessity and metaphysical possibility. There is the question whether his accounts are true, whether they count exactly the propositions they